Effect of (Mn,Cr) co-doping on structural, electronic and magnetic properties of zinc oxide by first-principles studies

Accepted Manuscript Effect of (Mn, Cr) co-doping on structural, electronic and magnetic properties of zinc oxide by first-principles studies D.E. Aimouch, S. Meskine, A. Boukortt, A. Zaoui PII: DOI: Reference:

S0304-8853(17)30063-X https://doi.org/10.1016/j.jmmm.2017.10.118 MAGMA 63334

To appear in:

Journal of Magnetism and Magnetic Materials

Received Date: Revised Date: Accepted Date:

7 January 2017 18 October 2017 28 October 2017

Please cite this article as: D.E. Aimouch, S. Meskine, A. Boukortt, A. Zaoui, Effect of (Mn, Cr) co-doping on structural, electronic and magnetic properties of zinc oxide by first-principles studies, Journal of Magnetism and Magnetic Materials (2017), doi: https://doi.org/10.1016/j.jmmm.2017.10.118

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Effect of (Mn, Cr) co-doping on structural, electronic and magnetic properties of zinc oxide by first-principles studies D.E. Aimouch1*, S. Meskine1, A. Boukortt1 and A. Zaoui2 Laboratoire d’Elaboration et Caractérisation Physico Mécanique et Métallurgique des Matériaux (ECP3M), Département Génie Electrique, Faculté des Sciences et de la Technologie, Université Abdelhamid Ibn Badis de Mostaganem, 27000 Mostaganem, Algérie 1

2

Laboratoire de Physique Computationnelle des Matériaux, Université Djillali Liabès de Sidi Bel-Abbès, Sidi Bel-Abbès 22000, Algeria. *

[email protected],

Abstract In this study, structural, electronic and magnetic properties of Mn doped (ZnO:Mn) and (Mn, Cr) co-doped zinc oxide (ZnO:(Mn,Cr)) have been calculated with the FP-LAPW method by using the LSDA and LSDA+U approximations. Going through three configurations of Mn,Cr co-doped ZnO corresponding to three different distances between manganese and chromium, we have analyzed that ZnO:(Mn,Cr) system is more stable in its preferred configuration2. The lattice constant of undoped ZnO that has been calculated in this study is in a good agreement with the experimental and theoretical values. It was found to be increased by doping with Mn or (Mn, Cr) impurities. The band structure calculations showed the metallic character of Mn doped and Mn,Cr co-doped ZnO. As results, by using LSDA+U (U=6eV), we show the halfmetallic character of ZnO:Mn and ZnO:Mn,Cr. We present the calculated exchange couplings d-d of Mn doped ZnO which is in a good agreement with the former FPLO calculation data and the magnetization step measurement of the experimental work. The magnetic coupling between neighboring Mn impurities in ZnO is found to be antiferromagnetic. In the case of (Mn,Cr) co-doped ZnO, the magnetic coupling between Mn and Cr impurities is found to be antiferromagnetic for configuration1 and 3, and ferromagnetic for configuration2. Thus, the ferromagnetic coupling is weak in ZnO:Mn. Chromium co-doping greatly enhance the ferromagnetism, especially when using configuration2. At last, we present the 2D and 3D spin-density distribution of ZnO:Mn and ZnO:(Mn,Cr) where the ferromagnetic state in ZnO:(Mn,Cr) comes from the strong p–d and d-d interactions between 2p-O, 3d-Mn and 3dCr electrons. The results of our calculations suggest that the co-doping ZnO(Mn, Cr) can be among DMS behavior for spintronic applications. Keywords: ZnO:Mn, ZnO:(Mn,Cr), DMSs, ferromagnetic, antiferromagnetic

1. Introduction II–VI semiconductors compounds have been extensively studied because of their high performance for optoelectronic devices. They usually cover the light spectrum from UV to the visible region. Zinc oxide (ZnO) is one of the most important II-VI semiconductors used for optoelectronic applications. ZnO have attracted much attention because of its wide direct band gap (3.3eV) and its large exciton binding energy of 60 meV at room temperature. Zinc oxide is suitable for different optoelectronic devices, such as gas sensors [1,2], dye-sensitized solar cells [3], photonic devices [4], laser systems, light emitting diodes[5], flexible displays [6] and surface acoustic wave devices [7]. It was synthesized using a different method, such a ssol-gel route [8], the combination of chemical and thermal annealing techniques [9], the combustion reaction method [10], chemical vapor deposition (CVD) and chemical bath deposition (CBD) [11]. Furthermore, ZnO has been found stable in its preferred wurtzite structure [12-14]. It is well known that ZnO is a n-type semiconductor. Many experimental works have been done to render it p-type, by doping with different materials such as transition metal elements. Salmani et al. used the Korringa–Kohn–Rostoker method combined with the coherent potential approximation (KKR–CPA) to calculate the electronic structure of Mn doped ZnO. The authors achieved to p-type material by using Mn doping on ZnO compound and they explained their electrical properties successfully [15]. Moreover, many researchers have investigated the effect of some dopants in zinc oxide, for example Nickel (Ni) [16], Cobalt (Co) [17], Manganese (Mn) [18], Titanium (Ti) [19], Vanadium (V) [20], Iron (Fe) [21] in order to tune the electrical, magnetic and optical properties of ZnO. Zinc oxide was co-doped with two different materials such as Magnesium and Aluminum (Mg-Al) [22], Manganese and Sodium (Mn-Na) [23], Cerium and Manganese (Ce-Mn) [24]. Although, ZnO-based diluted magnetic semiconductors (DMSs) were found as exhibiting ferromagnetic behavior, which means that they are promising materials to be employed in spintronic applications. However, the origin of ferromagnetism in ZnO-based DMSs depends on the type of impurities introduced into ZnO host material. The ferromagnetic phase of ZnO-based DMSs has been investigated by numerous previous works. In general, diluted magnetic semiconductor materials reveal the ferromagnetic state at room temperature and above. However, the source of this FM state is quiet ambiguous. For example, Fe doped ZnO clusters [25], the spinel phase in (ZnMn2O4, ZnCo2O4) [26] were considerably induced the FM behavior. More recently, Jayakumar et al. reported that the appearance of ferromagnetism in Mn doped ZnO is revealed by secondary peaks [27]. Also, The curie temperature ferromagnetism has been observed in Mn doped ZnO [28, 29]. Therefore, many experimental results have been claimed, such as the low Curie temperature [30], spin-glass character [31], and the existence of antiferromagnetism [32]. Hence, some experimental results included the transition metals (TM) co-doping diluted magnetic semiconductors. Singhalet al. [33] reported that the co-doping of Mn into Co doped ZnO enhances the ferromagnetic arrangement. Aljawfiet al. [34] suggested that the ferromagnetism of chromium and cobalt codoped zinc oxide improve when the Cr doping increases. Moreover, the d–d interaction especially the exchange coupling of 3d transition metals in ZnO has been extensively studied for their important magnetic and optical properties. However, the d-d exchange coupling between 3d levels of transition metals impurities might occurs the ferromagnetic character in ZnO bulk. Usman Ilyes et al. reported that the origin of ferromagnetic comes mainly from Mn-defect pair exchange coupling with oxygen interstitials in host ZnO matrix [35]. The exchange coupling between s-p states of host material (ZnO) and d states of transition metal elements leads to obvious change in the electrical, optical, and magnetic properties of the material [36].

In this paper, the structural, electronic and magnetic properties of Mn doped ZnO (ZnO:Mn) and Mn,Cr co-doped ZnO (ZnO:(Mn,Cr)) are calculated with the FP-LAPW method by using LSDA and LSDA+U approximations. We show three configurations of Mn,Cr co-doped ZnO corresponding to three different distances between manganese and chromium. We focus our study on two main points, (I) the ferromagnetism investigation in Mn doped ZnO and its stabilization by Cr co-doping. (II) The origin of ferromagnetism in Mn,Cr co-doped ZnO diluted magnetic semiconductor. 2. Method of calculation We used FP-LAPW method (full-potential linearized augmented-plane wave) [37], with the local spin density approximation (LSDA) as well as the LSDA+U were used to calculate the electronic and magnetic properties of Mn doped and Mn,Cr co-doped ZnO. We have chosen U=6eV and U=4.5eV for Mn and Cr elements [38, 39]. The wurtzit structure of ZnO is containing 32 atoms, 16 atoms of Zn and 16 atoms of O. Subsequently, two atoms of Zn were substituted by two Mn atoms, to obtain the system ZnO:Mn corresponding to a doping concentration of 12.5% of Mn. Two atoms of Zn were substituted by one Mn atom and one Cr atom, to obtain the system ZnO:(Mn,Cr) corresponding to a doping concentration of 12.5% of (Mn,Cr). The RMT*Kmax parameter is set to 7.0, where Kmax is the plane wave cut-off and RMT the smallest of all MT sphere radii. The muffin-tin radii values of Zn, O, Mn and Cr are set to 2.0, 1.6, 2.0 and 2.0 respectively. We used 200 K-points for both concentrations of 12.5% Mn and 12.5% Mn,Cr. The crystalline structure of undoped ZnO is formed by two atoms with space group P63-cm6 (wurtzite structure). The crystalline structure with two atoms of Mn or of Mn,Cr in the 32 atoms supercell has no corresponding hexagonal symmetry. Min Zhong et al. prepared the Mn,Cr co-doped ZnO successfully, they confirmed by X-ray diffraction and Raman spectra that all the samples have hexagonal wurtzite structure [40]. Furthermore, we present in this study three configurations of Mn,Cr co-doped ZnO, which corresponds to three different distances between Mn and Cr atoms (see in Fig. 1).The distances between Mn and Cr atoms are given as follows: d1=3.136 Å presenting the configuration1 (C1), d2=3.177 Å presenting the configuration2 (C2), and d3=5.206 Å presenting the configuration3 (C3).

Fig. 1: The crystalline structure of ZnO:(Mn,Cr) for (a) configuration1 (C1), (b) configuration2 (C2) and (c) configuration3 (C3)

Results and discussion 1. Structural properties The lattice parameter and the cell volume of ZnO:Mn and ZnO:(Mn,Cr) are listed in table 1 were giving by fitting the total energies to Murnaghan equation state. The calculated total energy of all systems is depicted in Fig. 2. The distance between the dopants doesn’t influence the total energy of the material. In contrast, the size of the cells is satisfactory to have a different magnetism for each configuration as will be explained in the magnetic properties section. The lattice parameter of undoped ZnO is a=3.207 Å and c=5.148 Å, which is in a good agreement with theoretical and experimental woks [41-43]. The lattice parameter is found to be increased by doping with Mn impurity and its value is for the ferromagnetic configuration a=3.222Å and c=5.161Å due to the smaller ionic radius of Zn2+(0.74Å) than that of Mn2+(0.83Å). This tendency was found experimentally [44]. Also Pazhanivelu et al reported that the lattice parameter and unit cell volume of Mn incorporated into ZnO are higher than that of undoped ZnO, due to the fact that the substitution of larger ion Mn2+(0.83 Å) in smaller ionic places Zn2+(0.74 Å) [45]. In the case of ZnO:(Mn,Cr), the lattice parameter for the ferromagnetic configurations values are a=3.213 Å and c=5.146 Å, a=3.214 Å and c=5.148, a=3.210 Å and c=5.156 Å for C1, C2 and C3 respectively (see in Tab. 1).

Fig.2 The optimized energy of (a) Mn doped ZnO, and (a), (b), (c) Mn,Cr co-doped ZnO for C1, C2, C3 respectively

Table.1 The lattice parameter (Å) and cell volume (Å3) of undoped ZnO, ZnO:Mn and ZnO:(Mn,Cr) (C1,C2,C3). Systems

a (Å)

c (Å)

c/a

Cell volume (Å3)

ZnO

3.207

5.148

1.605

45.853

3.252a

5.215a

1.603a

47.780a

3.201b

5.128b

1.601b

45.504b

3.189c

5.163c

1.619c

45.471c

3.222

5.161

1.602

46.340

3.255d

5.212d

1.601d

47.817d

C1

3.213

5.146

1.602

46.007

C2

3.214

5.148

1.602

46.053

C3

3.210

5.156

1.606

46.010

ZnO:Mn

a

. Experimental work Ref [41]. . Theoretical work Ref [42]. c . Theoretical work Ref [43]. d . Experimental work Ref [44]. b

2. Electronic properties We present the band structure of ferromagnetic compounds Mn doped and Mn,Cr co-doped ZnO for both directions of spin in Fig. 3. The gap value of undoped ZnO is 0.86 as found in our previous work [37]. For Mn doped ZnO, it is obvious that the conduction band minimum (CBM) and the valence band maximum (VBM) are overlapping for spin up channel, while the CBM crosses the Fermi level for spin down channel. So there is no gap for both directions of spin, and the material have a metallic character due to Mn impurity. In the case of the band structure of ZnO:Mn based on LSDA+U calculations. The material shows spin polarization phenomenon because it have the metallic behavior for spin up, and an insulating character for spin down. This result agrees well with that found in the literature [46]. Moreover, for spin up channel, there is a strong electronic coupling between the magnetic ions and charge carriers at Fermi level. Obviously, the 3d-Mn states significantly overlap with the 2p-O states in the region near the Fermi level (EF), indicating a strong p-d hybridization between them. In the case of Mn,Cr co-doped ZnO, the both conduction and valence band are overlapping for spin up channel for all three configurations. In spin down channel, the maximum valence band is 2.25eV, -2.30eV and -2.18eV for configuration1, configuration2 and configuration3 from the smallest Mn-Cr distance to the larger one respectively. Nevertheless, the same metallic character is obvious for Mn,Cr co-doped ZnO with a zero energy gap. In the case of the band structure of ZnO:(Mn,Cr) based on LSDA+U calculations. The material shows half-metallic character for all three configurations, because it has the metallic behavior for spin up, and an insulating character for spin down. This half-metallic character probably makes this compound promising candidate for applications in spintronic.

Fig.3: The band structure of ZnO:Mn and ZnO:(Mn,Cr) calculated with LSDA (a), (c), (e), (g), (i), (k), (m), (o) and LSDA+U (b), (d), (f), (h), (j), (l), (n), (p)

The total and partial densities of states of ferromagnetic Mn doped and Mn,Cr co-doped ZnO are shown in Fig. 4. In the case of ZnO:Mn, the density of states in the range -3 eV and 0 eV for spin up channel, and between 0 eV and 3 eV for spin down channel are dominated by 3dMn states. Whereas, there is no gap for both directions of spin, and the material have a metallic character (see in Fig. 4.a). In contrast, by using LSDA+U calculations, ZnO:Mn shows the half-metallic character (see in Fig. 4.b). This property was found experimentally [46]. For ZnO:(Mn,Cr), the total density of states shows the metallic character for all three configurations. It can be seen that the energy range between -3 eV and 0 eV in spin up and between 0 eV and 3 eV in spin down is mostly dominated by 3d-Mn and 3d-Cr states. The localized peak around the Fermi level comes mainly from 3d-Cr impurity. That peak is more localized in the first configuration (C1) (see in Fig. 4.c). The VBM and the CBM of ZnO:(Mn,Cr) are shifted towards the higher energy by increasing the distance between Mn and Cr atoms. Moreover, in the case of the densities of states of ZnO:(Mn,Cr) based on LSDA+U calculations. The material shows half-metallic character because it has the metallic behavior for spin up, and an insulating character for spin down as found in the band structure part (see in Fig. 4.d). Furthermore, d-Mn and d-Cr states are depicted in Fig. 4. e, f, g, h. We observe that 3d-Mn states contribute slightly in spin up around the Fermi level for C1. 3d-Cr states contribute mostly in spin up around the Fermi level for C1 and C3 (see in Fig. 4(g)). Nevertheless, Hubbard splitting occurs in the d band of Mn and Cr. Furthermore, the magnetic moments are mainly contributed by the 3d-Mn, 3d-Cr and 2p-O orbitals. The holes introduced by Mn,Cr dopants are the major carriers, especially when the O atoms nearest to the Mn or Cr dopants corroborate the ferromagnetic (FM) coupling, since the 2p-O states hybridize with the 3d-Mn and 3d-Cr states. Thus, the p-d hybridizations lead to the formation of FM phase in Mn,Cr co-doped ZnO compound.

Figure 4: The total and partial densities of states of ZnO:Mn and ZnO:(Mn,Cr) calculated with LSDA (a), (c), (e), (g) and LSDA+U (b), (d), (f), (h)

3. Magnetic properties To examine the type and strength of magnetic coupling between Mn or Mn,Cr dopants, we replaced two Zn atoms with Mn pairs for ZnO:Mn, and with Mn,Cr atoms for ZnO:(Mn,Cr). Several configurations were calculated for ZnO:(Mn,Cr). Two different magnetic configurations were analyzed. In one magnetic configuration the Mn-Mn atoms (ZnO:Mn) and Mn-Cr atoms (ZnO:(Mn,Cr)), had parallel spin orientation and we further refer to it as a ferromagnetic configuration. In the second one, antiparallel couplings between Mn-Mn and Mn-Cr were investigated and we will quote it as an antiferromagnetic configuration. Table 2 lists the energy difference between the ferromagnetic (FM) and antiferromagnetic (AFM) arrangement to define the coupling state of ZnO:Mn and ZnO:(Mn,Cr). We calculate the nearest neighbor exchange couplings Jdd between two Mn ions for ZnO:Mn, and between Mn and Cr ions for ZnO:(Mn,Cr) for each configuration. The Heisenberg Hamiltonian for a localized spin pair is defined by [47]

and leads to the following energy difference between the ferromagnetic and antiferromagnetic total energies EFM and EAFM [48]

where ST is the total magnetic moment of the two localized spins. ST =5 or 4 for Mn or Cr, respectively. The energy difference between the FM and AFM arrangement is negative for ZnO:Mn as well as for configuration C1 and C3, while it is positive for configuration C2 (see Table 2). The negative sign means that two neighboring spins arrange themselves antiferromagnetically, while the positive sign means that two neighboring spins prefer a ferromagnetic arrangement. ZnO:Mn have the antiferromagnetic behavior. In the case of ZnO:(Mn,Cr), the AFM state is energetically more stable in C1 and C3, but C2 is FM. Many experimental works have been focused on obtaining the room temperature ferromagnetic (RTFM) in Mn-doped ZnO. Conversely, many contradictory studies reported that Mn doped ZnO was found to be ferromagnetic [49], paramagnetic [50, 51], antiferromagnetic [52] or diamagnetic [53]. The important raison of those different results is that the growth conditions and the experimental methods are different. The oxygen vacancy also play an important role in RTFM of DMS materials, for example in transition metals (Co, Cu, Ni, Fe and Mn) doped ZnO [54-58]. The interstitial defect in Cu, Na co-doped ZnO enhance the ferromagnetism in the material [59]. Kumar et al. reported ferromagnetism in Fe doped ZnO due to the charge mediation [60]. Furthermore, the calculated energy difference ΔE between the ferromagnetic and antiferromagnetic state is found close to other calculation [61]. By using LSDA+U calculation, the

exchange couplings Jdd between Mn pairs is in a good agreement with the former FPLO data [62] and the experimental work [63]. The RKKY theory shows the exchange interaction between localized spins and s-p electron of host material, which are the origin of the RTFM behavior in diluted magnetic semiconductor materials [64, 65]. Coey et al. reported the exchange interaction between TM-O-TM, which lead to RTFM of material [66]. In this study, the ferromagnetic coupling of ZnO:(Mn,Cr) is absolutely found in configuration2. Mn and Cr impurities in configuration2 are doped along X-Y axis. So the distance between Mn and Cr elements and the plan area of Mn,Cr co-doping play an important role to enhance the ferromagnetic couplings of ZnO:(Mn,Cr). The ferromagnetic state was obtained in group I element doped ZnO by using Zn interstitial and O vacancy [67]. Also, the room temparture

ferromagnetic was found in non-magnetic ions doped ZnO [68]. In our previous work, we have successfully doped ZnO with non-magnetic impurity (potassium), subsequently, we have obtained the ferromagnetic behavior in K doped ZnO [69]. Tab. 2 The distance between Mn,Cr impurity (dMn-Cr), the energy difference ΔE, the d-d exchange coupling Jdd, the ferromagnetic stability (coupling) of ZnO:Mn and ZnO:(Mn,Cr). ZnO:(Mn,Cr) dMn,Cr(Å) Coupling ΔE(meV)/Mn

Jdd(meV)/Mn

LSDA LSDA+U LSDA LSDA+U

ZnO:Mn AFM -125.059 -60.990 -109.5a -4.169 -2.033 -2.000b -2.180c -2.090d

C1 3.136 AFM -39.102 -0.418 -1.955 -0.021

C2 3.177 FM 7.836 2.105 0.392 0.105

C3 5.206 AFM -152.126 -10.580 -7.606 -0.529

-

-

-

a

. Theoretical work Ref [61]. . Theoretical work Ref [38]. c . Theoretical work Ref [62]. d . Experimental work Ref [63]. b

The total and local magnetic moments of the ferromagnetic configuration for both Mn doped and Mn,Cr co-doped ZnO compounds are shown in Table 3. The spin-polarized calculations indicate that Mn or Mn,Cr dopants induce a local magnetic moment of about 3.975 μβ for ZnO:Mn and 6.622 μβ, 6.633 μβ and 6.367 μβ per supercell for C1, C2 and C3 respectively. The magnetic moments of the Mn pair atoms take percentages of 81.31% in the total net magnetic moments of ZnO:Mn, while the magnetic moment of the Mn,Cr pair atoms take percentage of 77,66%, 77.58% and 74.62% for C1, C2 and C3 respectively. By using LSDA+U (see in Tab. 4), the local magnetic moment of Mn increases, neither for Cr elements in ZnO:(Mn,Cr). Furthermore, it can be seen that the total magnetic moment is decreased by substituting one Mn by one Cr impurity, due to the smaller magnetic moment of Cr element (2.8 μβ) than Mn element (3.8μβ). In addition, the total magnetic moment is almost the same for all three configurations, and the local magnetic moment of Mn elements decreases by increasing distance between Mn and Cr impurities (see Table 3). Nevertheless, in the case of the antiferromagnetic configuration, the total magnetic moment of ZnO:Mn is completely compensated due to the similar neighborhood and atomic nature (Mn). In the case of ZnO:Mn, Cr the total magnetic moment is equal to -1.341, -1.324, -1.326 µB for C1, C2, C3 respectively, because the doping is realized with two different atoms having different radii and electronic configurations, which also provides different neighborhoods.

Tab. 3 The total magnetic moment μtot and local magnetic moment Mn, Cr, Zn, O et μint (interstitial) of the ferromagnetic and antiferromagnetic states ZnO:Mn and ZnO:(Mn,Cr) calculated with LSDA. Ferromagnetic ZnO:Mn C1 C2 Mn(μβ) 3.975 3.821 3.853 3.975 Cr(μβ) 2.801 2.780 Zn(μβ) 0.024 0.001 0.001 O(μβ) 0.113 0.020 0.076 μint(μβ) 1.138 1.427 1.437 μtot(μβ) 9.777 8.526 8.550

C3 3.533 2.834 0.019 0.084 1.424 8.533

Antiferromagnetic ZnO:Mn C1 C2 3.907 -3.824 -3.826 -3.907 2.735 2.746 -0.005 -0.010 -0.010 0.005 0.006 0.007 -0.064 -0.069 -0.063 0.064 0.021 0.024 0.000 -0.048 -0.067 0.000 -1.341 -1.324

C3 -3.738 2.654 -0.004 0.002 -0.070 0.013 -0.062 -1.326

Tab. 4 The total magnetic moment μtot and local magnetic moment Mn, Cr, Zn, O et μint (interstitial) of the ferromagnetic and antiferromagnetic states ZnO:Mn and ZnO:(Mn,Cr) calculated with LSDA+U. Ferromagnetic ZnO:Mn C1 C2 Mn(μβ) 4.377 4.204 4.208 4.377 Cr(μβ) 2.941 2.944 Zn(μβ) 0.013 0.009 0.008 O(μβ) 0.053 0.047 0.036 μint(μβ) 0.941 1.312 1.284 μtot(μβ) 9.999 8.758 8.746

C3 4.193 2.980 0.014 0.037 1.344 8.804

Antiferromagnetic ZnO:Mn C1 C2 -4.362 -4.201 -4.209 4.362 2.951 2.964 -0.003 -0.005 -0.005 0.003 0.007 0.008 -0.030 -0.029 -0.030 0.030 0.018 0.018 0.000 0.080 0.051 0.000 -1.193 -1.227

C3 -4.186 2.512 -0.001 0.003 -0.030 0.012 0.072 -1.211

To clarify better the origin of spin polarization induced by Mn and Mn,Cr dopants, the isosurfaces of electron spin density of the ferromagnetic state of Mn doped and Mn,Cr co-doped ZnO are plotted in Fig. 5. It is clear that polarized spins are mainly located on Mn and Cr atoms and its nearest-neighboring four O atoms, and next-neighboring Zn atoms. The spindensity contour and iso-surface spin-density plot of each configuration of ZnO:(Mn,Cr) are illustrated in Fig. 5. This figure obviously shows a strongly localized spin polarization nearby O atoms surrounding Mn and Cr atoms. That localized spin polarization presents the local magnetic moments in ZnO:(Mn,Cr). The slice is selected passing through Mn, Cr and O for C1 and C2, and through Mn, Cr, O, Zn for C3. From the two-dimensional distribution of the spin-density, it can be seen that both Mn,Cr atoms and their O neighbors are spin polarized, and O neighbors of Mn carry larger magnetizations than that of Cr element. One thinks that the strong p-d and d-d interaction in this case, participates in the appearance of ferromagnetism in ZnO:Mn and ZnO:Mn,Cr and mainly due to the defects in host matrix or to the defects in incorporation of Manganese and Chrome ions substituting for Zn in the ZnO. The Cr-doped magnetic behavior ZnO can be caused by the double exchange in the case of Cr3+ and the Super-exchange mechanism for Cr2+. Moreover, the next-neighboring Zn atoms are almost not spin-polarized. The magnetic moment of Zn is very small and its value is 0.001μβ, 0.001μβ and 0.019μβ for C1, C2 and C3 respectively even though the magnetic moment of Mn and Cr is about 3.8 μβ (see Table 3).The neighboring O atoms have the magnetizations of 0.020 μβ, 0.076 μβ and 0.084 μβ for C1, C2 and C3 respectively. This is

quite similar as found in the case of Mn doped GaN where the magnetization on atoms neighboring Mn is small even though the Mn has a magnetization of 4 μβ [70]. R. Q. Wu et al. studied the magnetic properties of Cu doped GaN. The authors showed that the magnetic moment comes mainly from the CuN4 tetrahedron site, even though Cu and N both are nonmagnetic atoms in their nature phases [71].

Fig. 5 (a), (b), (c) Two-dimensional distribution of spin-density, and (d), (e), (f) Iso-surface spin-density plot (at an isovalue of 0.003 e/Å3) of Mn, Cr co-doped ZnO for C1, C2, C3 respectively using LSDA+U.

Conclusion In this paper, we investigated the effect of Mn doping and (Mn,Cr) co-doping on the structural, electronic and magnetic properties of zinc oxide by using the first-principles and FPLAPW method with LSDA and LSDA+U approximations. Our results showed three configurations corresponding to three different distances between Mn and Cr impurities. The lattice parameter was found to be in a good agreement with theoretical and experimental woks [41-43] and it was increased by doping with Mn and co-doping with Cr impurities, this tendency was found experimentally for Mn doped ZnO [44,45]. The band structure and the density of states of Mn doped and (Mn,Cr) co-doped ZnO were presented and interpreted. In the case of LSD+U calculation, ZnO:Mn and ZnO:(Mn,Cr) show the half-metallic character.

This property was found experimentally [46]. That property makes our compound as a promising material for the future spintronic devices. We showed the antiferromagnetic phase of ZnO:Mn as found in the literature [62]. Therefore, we have presented the nearest neighbor exchange couplings Jdd between two Mn ions for ZnO:Mn, and between Mn and Cr ions for ZnO:(Mn,Cr) by using the Heisenberg Hamiltonian for a localized spin pair. By using U=6eV applied on d-Mn states, we have found the exchange couplings of Mn pairs in a good agreement with the former FPLO data [62] and the magnetization step measurement [63]. The antiferromagnetic behavior of ZnO:Mn is dominated. In the case of ZnO:(Mn,Cr), the AFM state is energetically more stable in C1 and C3, but C2 is FM. Therefore, we presented the 2D and 3D spin-density distribution of ZnO:Mn and ZnO:(Mn,Cr) to clarify better the origin of the ferromagnetism. We have found that the ferromagnetic state of ZnO:(Mn,Cr) comes mainly from The strong p–d and d-d interactions between 2p-O, 3d-Mn and 3d-Cr electrons. To summarize, Cr co-doping greatly enhance the ferromagnetism in configuration2 of ZnO:(Mn,Cr). That compound might be a convenient material for novel spintronic devices. Acknowledgement The authors are very grateful to financial support provided by ECP3M laboratory, University of Mostaganem, Algeria. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Y. Caglar, S. Aksoy, S. Ilican, M. Caglar, Superlatt. Microstruct. 46 (2009) 469–475. S.C. Navale, I.S. Mulla, Mater. Sci. Eng. C 29 (2009) 1317–1320. A. Mejda, M. Castagné, N.K. Turki, Superlatt. Microstruct. 53 (2013) 213–222. S. Benkara, S. Zerkout, H. Ghamri, Mater. Sci. Semicond. Process. 16 (2013)1271–1279. N. Chahmat, T. Souier, A. Mokri, M. Bououdina, M.S. Aida, M. Ghers, J. Alloys Compd. 593 (2014) 148–153. C.Y. Tsay, H.C. Cheng, Y.T. Tung, W.H. Tuan, C.K. Lin, Thin Solid Films 517(2008) 1032–1036. C. Aydin, M.S. Abd El-Sadek, I.S. Kaibo Zheng, Y.F. Yakuphanoglu, Opt. LaserTechnol. 48 (2013) 447–452. R. Dhahri, M. Hjiri, L.El.Mira, A.Bonavitab, D. Iannazzob, S.G. Leonardi, G. Neri, Applied Surface Science 355 (2015)1321–1326. M. Simaa, M. Baibaraca, E.Vasileb, Ma. Simaa, L. Mihut, Applied Surface Science 355 (2015)1057–1062. A. Franco Jr, H.V.S. Pessoni, Physica B 476 (2015) 12–18. Ruey-Chi Wang, Wei-Sung Su, Journal of Alloys and Compounds 654 (2016) 1e7. D.N. Papadimitriou, Thin Solid Films,605 (2015) 215–231. A. Mallick, S. Sarkar, T. Ghosh, D.Basak, Journal of Alloys andCompounds 646 (2015) 56e62. H. Aydina, H.M. El-Nasserb, C. Aydinc, Ahmed. A. Al-Ghamdi, F. Yakuphanoglu, Applied Surface Science 350 (2015)109–114. E. Salmani, A. Benyoussef, H. Ez-Zahraouy, Chin. Phys. B, 21, (2012) 106601. , E. H. Saidi b) , and O. Mounkachi c) Phys. Rev. B,63(2001) 195205. Liu-Niu Tong, Xian-Mei He, Huai-Bin Hana, Jin-Lian Hua, Ai-Lin Xia, Yan Tong, Solid State Communications 150 (2001)00120016. S. Caliskan, S. Guner, Journal of Alloys and Compounds 619 (2015) 91–97. BakhtiarUlHaq, R. Ahmed, A. Shaari, A. Afaq, B.A. Tahir, R. Khenata, Materials Science in Semiconductor Processing 29 (2015) 256–261. Z. Weng, Z. Huang, W. Lin, Physica B 407 (2012) 743–747.

21. Q.B. Wang, C. Zhou, J. Wu, T. Lu, Optics Communications 297 (2013) 79–84. 22. BakhtiarUlHaq, R. Ahmed, A. Shaari, N. Ali, Y. Al-Douri, A.H. Reshak, Materials Science in Semiconductor Processing 43 (2016) 123–128. 23. Xiaodong Si, Yongsheng Liu, Wei Lei, Juan Xu, Wenlong Du, Jia Lin,Tao Zhou, Li Zheng, JMADE 1057(2015). 24. Kai-Cheng Zhang, Yong-Feng Li, Yong Liu, Yan Zhu, Physica B 451 (2014) 43–47. 25. J. E. Ramos, M. Montero-Munoz, J. A. H. Coaquira, J. E. Rodrıguez-Paez, J. Appl. Phy. 115 (2014) 17E123. 26. K. Samanta, P. Bhattacharya, R. S. Katiyar, Phy. Rev. B. 73 (2006) 245213. 27. O. D. Jayakumar, H. G. Salunke, R. M. Kadam, M. Mohapatra, G. Yaswant, S. K.Kulshreshtha, Nanotechnology. 17 (2006) 1278. 28. S.-W. Lim, M.-C. Jeong, M.-H. Ham, Ham, J.-M. Myoung, J. Appl. Phys. 43 (2004) L280. 29. Y. Heo, M. Ivill, K. Ip, D. Norton, S. Pearton, J. Kelly, R. Rairigh, A. Hebard, T. Steiner, Appl. Phys. Lett. 84 (2004) 2292-2294. 30. Y. Chang, D. Wang, X. Luo, X. Xu, X. Chen, L. Li, C. Chen, R. Wang, J. Xu, D. Yu, Appl. Phys. Lett. 83(2003) 4020-4022. 31. T. Fukumura, Z. Jin, M. Kawasaki, T. Shono, T. Hasegawa, S. Koshihara, H. Koinuma, Appl. Phys. Lett. 78 (2001) 958-960. 32. M. Bouloudenine, N. Viart, S. Colis, J. Kortus, A. Dinia, Appl. Phys. Lett. 87 (2005) 052501-052501. 33. R. Singhal, A. Samariya, S. Kumar, Y. Xing, U. Deshpande, T. Shripathi, S. Dolia, E.B. Saitovitch, Phys. Status Solidi A,207 (2010) 2373-2386. 34. R.N. Aljawfi, F. Rahman, K.M. Batoo, J. Magn. Magn. Mater. 332 (2013) 130-136. 35. J. Arul Mary, J. Judith Vijaya, J.H. Dai, M. Bououdina, L. John Kennedy,Y. Song, Materials Science in Semiconductor Processing 34 (2015) 27. 36. A. Goktas, I.H. Mutlu, Y. Yamada, E. Celik, J.Alloy. Compd. 553 (2013) 259. 37. D.E. Aimouch, S. Meskine, Y. Benaissa Cherif, A. Zaoui, A. Boukortt, Optik130 (2017) 1320–1326. 38. T. Chanier, M. Sargolzaei, I. Opahle, R. Hayn, and K. Koepernik, arXiv:condmat/0511050. 39. Priya Gopal and Nicola A. Spaldin, arxiv.org/abs/cond-mat/0605543v1. 40. Min Zhong, Ying Li, Yemin Hu, Mingyuan Zhu, Wenxian Li, Hongmin Jin, Shiwei Wang, Yibing Li, Huijun Zhao, J. Alloy. Compd.647, (2015) 823. 41. J. Sivasankari, S. Sankar, L. VimalaDevi, J Mater Sci: Mater Electron, DOI:10.1007/s10854-015-3467-4. 42. Dongwei Maa, ZhiWanga, HaitaoCuia, Jun Zenga, ChaozhengHeb, Zhansheng Luc, Sensors and Actuators. B 224 (2016) 372. 43. Y. Wang, X. Zhang, X. Meng, Y. Cao, F. Yang, J. Nan, Q. Song , Q. Huang, C. Wei, J.Zhang, Y. Zhao, Solar EnergyMaterials&SolarCells. 145(2016)171. 44. V. M. de Almeida1, A. Mesquita², A. O. de Zevallos3, N. C. Mamani3, P. P. Neves3, X. Gratens4 3 ,V. A. Chitta4, W. B. Ferraz5, A. C. Doriguetto3, A. C. S. Sabioni1, H. B. de Carvalh, J. Alloy. Compd. 655, (2016) 406–414. 45. V.Pazhanivelua, A.PaulBlessingtonSelvaduraia, YongshengZhaob, R.Thiyagarajanb, R.Murugaraj, Physica B:Physics of Condensed Matter, 481, (2016) 91-96. 46. S. Lisenkov, A. N. Andriotis, R. M. Sheetz, M. Menon, PHYSICAL REVIEW B 83, (2011) 235203. 47. F. Matsukura, H. Ohno, A. Shen, Y. Sugawara, Phys. Rev. B, 57 (1998) R2037. 48. K. Olejnik, M.H.S. Owen, V. Novák, J. Mašek, A.C. Irvine, J. Wunderlich,T. Jungwirth, Phys. Rev. B,78 (2008) 054403.

49. Q.Y. Xu, H. Schmidt, L. Hartmann, H. Hochmuth, M. Lorenz, A. Setzer, P.Esquinazi, C. Meinecke, M. Grundmann, Appl. Phys. Lett. 91 (2007) 092503. 50. T. Droubay, D. Keavney, T. Kaspar, S. Heald, C. Wang, C. Johnson, K. Whitaker, D.Gamelin, S. Chambers, Phys. Rev. B 79 (2009) 155203. 51. S. Gilliland, A. Segura, J.F. Sánchez-Royo, L.M. García, F. Bartolomé, J.A. Sans, G.Martínez-Criado, F. Jimenez-Villacorta, J. Appl. Phys. 108 (2010) 073922. 52. S. Banerjee, K. Rajendran, N. Gayathri, M. Sardar, S. Senthilkumar, V. Sengodan,J. Appl. Phys. 104 (2008) 043913. 53. X.M. Cheng, C.L. Chien, J. Appl. Phys. 93 (2003) 7876. 54. Ting Guo, Yujung Zhang, Yidong Luo, Ce-Wen Nan, Yuan-Hua Lin, J. Appl. Phys. 112(2012) 083916. 55. GunjanSrinet, Ravindra Kumar, VivekSajal, J. Appl. Phys. 114 (2013) 033912. 56. V. Pazhanivelu, A. Paul BlessingtonSelvadurai, R. Murugaraj, J. Supercond. Nov. Magn.28 (2015) 2575. 57. k. Samanta, K, P. Bhattacharya, R. S. Katiyar, J. Appl. Phys. 105 (2009) 113929. 58. HaoGu, Yinzhu Jiang, Yongbing Xu, Mi Yan, J. Appl. Phys.98 (2011) 012502. 59. Yanyan Wei, DengluHou, ShuangQiao, Congmian Zhen, Guide Tang, Physica B 404(2009) 2486. 60. S. Kumar, Y. J. Kim, B. H. Koo, S. K. Sharma, J. M. Vargas, M. Knobel, S. Gautam, K. H.Chae, D. K. Kim, Y. K. Kim, C. G. Lee, J. Appl. Phys. 105 (2009) 07C520. 61. Fuchun Zhang 1, Dandan Chao 1, Hongwei Cui 1, Weihu Zhang 1 and Weibin Zhang. Hengda Li, Xinzhong Liu, Zhigong Zheng, Nanomaterials 5, (2015) 885. 62. T. Chanier, F. Virot, and R. Hayn, PHYSICAL REVIEW B 79, (2009) 205204. 63. X. Gratens, V. Bindilatti, N. F. Oliveira, Jr., Y. Shapira, S. Foner,Z. Golacki, and T. E. Haas, Phys. Rev. B 69, (2004)125209. 64. Hengda Li, Xinzhong Liu, Zhigong Zheng, J. Magn. Magn. Mater. 372 (2014) 37. 65. J.M.D. Coey, A. Douvalis, C. Fitzgerald, M. Venkatesan, Appl. Phys. Lett. 84 (2004)1332. 66. V. Pazhanivelu, A. Paul BlessingtonSelvadurai, R. Murugaraj, Mater. Lett. 151 (2015) 112. 67. J.M.D. Coey, M. Venkatesan, P. Stamenov, C.B. Fitzgerald, L.S. Dorneles, Phys. Rev. B 72(2005) 024450. 68. C.D. Pemmaraju, S. Sanvito, Phys. Rev. Lett. 94 (2005) 217205. 69. D. E. Aimouch, S. Meskine, R. Hayn, A. Zaouiand A. Boukortt, Modern Physics Letters B, 30(2016) 1650291. 70. B. Sanyal, O. Bengone and S. Mirbit, Phys. Rev. B, 68(2003) 205210. 71. R. Q. Wu, G. W. Peng, L. Liu and Y. P. Feng, Appl. Phys. Lett.,89(2006) 062505.

Highlights

 The electronic and magnetic properties of ZnO:Mn and ZnO:(Mn,Cr) were studied;  The half-metallic character of the doped ZnO:Mn and

ZnO:(Mn,Cr)

compounds;  Cr co-doping considerably increases the ferromagnetism in ZnO:(Mn,Cr) according to a certain arrangement of dopants;  The strong p-d and d-d interactions participate in the appearance of ferromagnetism in ZnO:Mn and ZnO:(Mn,Cr). 72.